Differential cross sections, charge production asymmetry, and spin-density matrix elements for (2010) produced in 500 GeV/c π−-nucleon interactions
Introduction
(2010) (JP=1−) production is important to understanding the production of charm because 's are expected to dominate the charm cross section: their spin causes them to be favored threefold over the low-lying D mesons at high center of mass energies. Charm production is an interesting topic in its own right, being calculable in perturbative QCD [1]. There has also been interest in the intrinsic charm content of hadrons [2]. Finally, accurate simulations of charm production required by future experiments at the Tevatron, the LHC, and lepton colliders will depend on these measurements which can be used to tune Pythia [3] and other Monte Carlo simulation packages.
Since mesons have spin 1, we might expect the charm quark spin to be reflected in the meson. Spin retention is particularly strong for heavy quarks, where the usual stiffness of the spin vector under relativistic boosts may be expected to play a part [4]. In any case, there are many anomalies of spin and polarization. For instance, it is known that some hyperons are strongly polarized in some regions of production and not in others, the reasons for this behavior being still not completely understood [5]. It is also known that most of the spin of the proton is not carried by the valence quarks [6]. Copious production of a vector meson provides us with a unique opportunity to add new information on polarization, and we hope that these data will shed further light on hadron physics.
In this Letter, we report measurements of the production of (2010) in 500 GeV/c π−-nucleon interactions. Forward differential cross sections and production asymmetries have been measured as functions of Feynman-x (xF) and transverse momentum squared (pT2). The measurements are compared to Pythia Monte Carlo models. The differential distributions are fit to well-known functional forms and fit parameters are compared with previous measurements. Also, spin-density matrix elements were measured, again as functions of xF and pT2.
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Experiment and data sample
E791, a high statistics charm physics experiment, took data at Fermilab's Tagged Photon Laboratory during the 1991–1992 fixed-target run. The experiment [7] used an upgraded version of the two-magnet spectrometer previously used in E516, E691, and E769. A 500 GeV/cπ− beam was directed at five target foils: a 0.52 mm thick platinum foil, followed by four 1.56 mm thick carbon foils, with a typical spacing of 15 mm between foil centers. Tracks and vertices used hits in 23 silicon microstrip and 45
Differential production cross sections
For the differential cross section study, the data sample was divided into 12 bins each of xF and pT2. In the range −0.1<xF<0.4, the bins have a width of 0.05, and in the range 0.4<xF<0.6 the bins have a width of 0.1. In the range 0<pT2<2 (GeV/c)2 bins have a width of 0.5 (GeV/c)2, and in the range 2<pT2<10 (GeV/c)2 bins have a width of 1 (GeV/c)2. In each bin of xF or pT2, Q-value histograms were created. Random event mixing was used to model the background shape, and the background level
Charge asymmetry in production
The charge production asymmetry is defined by the parameter where and denote the production cross-sections, of and , respectively, and and denote the respective acceptance-corrected numbers of such particles observed.
Using the same fitting techniques and data sample as was used in the differential cross section study, the production asymmetry as functions of xF and pT2 are shown in Fig. 3.
Spin-density matrix elements
The polarization state of a spin 1 particle can be described by a complex 3×3 spin-density matrix. A complex 3×3 matrix has 18 real components, but hermiticity and the fact that Trρ=1 reduces this number to 8. Also, the 's are produced in a strong interaction where parity conservation further reduces this number to 4. The spin-density matrix when expressed in a helicity basis then takes this form [19] with ρ1−1 and of course ρ11 real.
From this, one can
Systematic errors
The systematic errors reported were determined by comparing results, either from various subsamples, or by analyzing the full sample in multiple ways. Differences in measurements of the number of observed signal events were then determined as fractions of statistical errors bin by bin. Root mean squares of these fractions were then used as estimates of the systematic error as a fraction of statistical error. Several possible sources of systematic error were considered, and those found to be
Conclusions
We have measured the differential cross sections of production as functions of xF and pT2. While the usual functional forms used by other experiments to parameterize their data (, ) do not describe our data well, Eq. (3) suggested by Frixione et al. provides an excellent fit over our full range of pT2 (χ2=8.4 for 9 degrees of freedom). The Pythia model tuned for the E791 analysis of D± production does describe the pT2 cross section much better than the default Pythia model.
We observe an
Acknowledgements
We gratefully acknowledge the assistance of the staffs of Fermilab and of all the participating institutions. This research was supported by the Brazilian Conselho Nacional de Desenvolvimento Cientı́fico e Technológio, CONACyT (Mexico), FAPEMIG (Brazil), the Israeli Academy of Sciences and Humanities, the US Department of Energy, the US–Israel Binational Science Foundation and the US National Science Foundation. Fermilab is operated by the Universities Research Association, Inc., under contract
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